Finite Group DatabasebetaFinite Group Databasebeta| order | 19716 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C53⋊(D31⋊C3) |
| unambiguous semidirect product | (C2×C53)⋊(D31⋊C3) |
| unambiguous semidirect product | (C2×C31⋊C3)⋊D53 |
| unambiguous semidirect product | (C2×D1643)⋊C3 |
| Fitting, socle | C2×C31×C53 ⋊ C2×C3 |
| derived, Hall | C31×C53 ⋊ C22×C3 |
| Hall | C2×D1643 ⋊ C3 |
| Hall | C53×C31⋊C3 ⋊ C22 |
| Hall | C31⋊C3 ⋊ C2×D53 |
| Sylow | C53 ⋊ C2×D31⋊C3 |
| Sylow | C31 ⋊ C2×C3×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C53⋊(D31⋊C3) |
| commutator, cosocle, hypocenter | C31×C53 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C31×C53 | C2×C3 |
| LCS | G ▷ C31×C53 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3286 |
698 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19716, 18);